Abstract : We study repeated games where players use an exponential learning scheme in order to adapt to an ever-changing environment. If the game's payoffs are subject to random perturbations, this scheme leads to a new stochastic version of the replicator dynamics that is quite different from the ``aggregate shocks'' approach of evolutionary game theory. Irrespective of the perturba- tions' magnitude, we find that strategies which are dominated (even iteratively) eventually become extinct and that the game's strict Nash equilibria are stochastically asymptotically stable. We complement our analysis by illustrating these results in the case of congestion games.
Type de document :
Article dans une revue
The Annals of Applied Probability, 2010, 20 (4), pp.1359-1388
https://hal.archives-ouvertes.fr/hal-01382306
Contributeur : Panayotis Mertikopoulos
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Soumis le : dimanche 16 octobre 2016 - 15:29:26
Dernière modification le : jeudi 8 novembre 2018 - 14:28:04
Panayotis Mertikopoulos, Aris L. Moustakas. The Emergence of Rational Behavior in the Presence of Stochastic Perturbations. The Annals of Applied Probability, 2010, 20 (4), pp.1359-1388. 〈hal-01382306〉
